Thermodynamic: Conservation of Energy Question

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SUMMARY

The discussion centers on a thermodynamic problem involving a mixing tank containing 50 kg of water at 25°C, with two inlet streams at 80°C and 50°C, and an outlet stream. The flow rates are 5 kg/min for each inlet and 10 kg/min for the outlet. The participants analyze the conservation of energy to determine the equilibrium temperature of the tank. The correct approach involves applying the principle of conservation of energy and the concept of heat capacity to find the final temperature of the mixed water.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically conservation of energy.
  • Knowledge of heat capacity and its application in thermal equilibrium calculations.
  • Familiarity with flow rate calculations in fluid dynamics.
  • Basic algebra for solving equations related to temperature and mass flow.
NEXT STEPS
  • Study the conservation of energy in thermodynamic systems.
  • Learn how to calculate equilibrium temperature using heat capacity formulas.
  • Explore fluid dynamics concepts related to flow rates and mixing processes.
  • Practice similar thermodynamic problems involving multiple streams and heat transfer.
USEFUL FOR

Students in thermodynamics, engineers working with fluid systems, and anyone involved in heat transfer analysis will benefit from this discussion.

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Homework Statement



The mixing tank shown here initially contains 50 kg of water at 25°C. Suddenly the two valves and the single outlet valve are opened so that two water streams, each with a flow rate of 5 kg/min, flow into the tank, and a single exit stream with a flow rate of 10 kg/min leaves the tank. The temperature of one inlet stream is 80°C, and that of the other is 50°C. the tank is well mixed, so that the temperature of the outlet stream is always the same as the temperature of the water in the tank.

My (wrong) approach

I let the final temperature be T, and tried to find the equilibrium temperature using heat capacity. However, I am unable to get the correct answer.
 
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